MOT–Σ* FPGA SPECTRAL RUNTIME ARCHITECTURE

Formal Specification of Spectral Observability, Koopman Reconstruction, RG Dynamics, and FPGA Realization

Version 1.0

Author:
Vitaliy (VIT-BAZ) Bazarov
ORCID: 0009-0007-9967-5807

ABSTRACT

This specification defines a realizable computational layer for the META-PHASE
OPERATOR THEORY (MOT) based on spectral representations, Koopman operator
theory, renormalization dynamics, and FPGA implementation.

The framework treats computation as controlled spectral evolution of a finite
effective mode space rather than classical Boolean state transitions.

The architecture provides:

- spectral observability,
- Koopman state reconstruction,
- RG-semigroup emulation,
- Θ-state estimation,
- spectral gap monitoring,
- attractor reconstruction,
- FPGA-based runtime realization.

The FPGA implementation serves as an engineering realization layer between
abstract MOT mathematics and experimentally testable spectral computation.